Representation errors and retrievals in linear and nonlinear data assimilation

This article shows how one can formulate the representation problem starting from Bayes’ theorem. The purpose of this article is to raise awareness of the formal solutions,so that approximations can be placed in a proper context. The representation errors appear in the likelihood, and the different possibilities for the representation of reality in model and observations are discussed, including nonlinear representation probability density functions. Specifically, the assumptions needed in the usual procedure to add a representation error covariance to the error covariance of the observations are discussed,and it is shown that, when several sub-grid observations are present, their mean still has a representation error ; socalled ‘superobbing’ does not resolve the issue. Connection is made to the off-line or on-line retrieval problem, providing a new simple proof of the equivalence of assimilating linear retrievals and original observations. Furthermore, it is shown how nonlinear retrievals can be assimilated without loss of information. Finally we discuss how errors in the observation operator model can be treated consistently in the Bayesian framework, connecting to previous work in this area.

Impact of variation in structure of condensed tannins from sainfoin (Onobrychis viciifolia) on in vitro ruminal methan production and fermentation characteristics

Our study investigated the effects of condensed tannins (CT) on rumen in vitro methane (CH4) production and fermentation characteristics by incubating lucerne in buffered rumen fluid in combination with different CT extracts at 0 (control), 40, 80 and 120 g CT/kg of substrate DM. Condensed tannins were extracted from four sainfoin accessions: Rees ‘A’, CPI63763, Cotswold Common and CPI63767. Gas production (GP) was measured using a fully automated GP apparatus with CH4 measured at distinct time points. Condensed tannins differed substantially in terms of polymer size and varied from 13 (Rees ‘A’) to 73 (CPI63767) mean degree of polymerization, but had relatively similar characteristics in terms of CT content, procyanidin: prodelphinidin (PC: PD) and cis:trans ratios. Compared to control, addition of CT from CPI63767 and CPI63763 at 80 and 120 g CT/kg of substrate DM reduced CH4 by 43% and 65%, and by 23% and 57%, respectively, after 24-h incubation. Similarly, CT from Rees ‘A’ and Cotswold Common reduced CH4 by 26% and 46%, and by 28% and 46% respectively. Addition of increasing level of CT linearly reduced the maximum rates of GP and CH4 production, and the estimated in vitro organic matter digestibility. There was a negative linear and quadratic (p < 0.01) relation between CT concentration and total volatile fatty acid (VFA) production. Inclusion of 80 and 120 g CT/kg of substrate DM reduced (p < 0.001) branched-chain VFA production and acetate: propionate ratio and was lowest for CPI63767. A decrease in proteolytic activity as indirectly shown by a change in VFA composition favouring a shift towards propionate and reduction in branched-chain VFA production varied with type of CT and was highest for CPI63767. In conclusion, these results suggest that tannin polymer size is an important factor affecting in vitro CH4 production which may be linked to the CT interaction with dietary substrate or microbial cells.

The psychology of containment: mis/representing emotional and behavioural difficulties in Australian schools

The number of students in special schools has increased at a rapid rate in some Australian states, due in part to increased enrolment under the categories of emotional disturbance (ED) and behaviour disorder (BD). Nonetheless, diagnostic distinctions between ED and BD are unclear. Moreover, despite international findings that students with particular backgrounds are over-represented in special schools, little is known about the backgrounds of students entering such settings in Australia. This study examined the government school enrolment data from New South Wales, the most populous of the Australian states. Linear and quadratic trends were used to describe the numbers and ages of students enrolled in special schools in the ED and BD categories. Changes between 1997 and 2007 were observed. Results showed an over-representation of boys that increased across the decade and a different pattern across age for boys and girls. Consistent with international findings, these results indicate that trends in special school placements are unrelated to disability prevalence in the population. Rather, it is suggested that schools act to preserve time and resources for others by removing their more challenging students: most typically, boys.

Evaluation of positioning error-induced pixel shifts on satellite linear push-broom imagery

Georeferencing is one of the major tasks of satellite-borne remote sensing. Compared to traditional indirect methods, direct georeferencing through a Global Positioning System/inertial navigation system requires fewer and simpler steps to obtain exterior orientation parameters of remotely sensed images. However, the pixel shift caused by geographic positioning error, which is generally derived from boresight angle as well as terrain topography variation, can have a great impact on the precision of georeferencing. The distribution of pixel shifts introduced by the positioning error on a satellite linear push-broom image is quantitatively analyzed. We use the variation of the object space coordinate to simulate different kinds of positioning errors and terrain topography. Then a total differential method was applied to establish a rigorous sensor model in order to mathematically obtain the relationship between pixel shift and positioning error. Finally, two simulation experiments are conducted using the imaging parameters of Chang’ E-1 satellite to evaluate two different kinds of positioning errors. The experimental results have shown that with the experimental parameters, the maximum pixel shift could reach 1.74 pixels. The proposed approach can be extended to a generic application for imaging error modeling in remote sensing with terrain variation.

An optimization problem concerning multiplicative functions

In this paper we study the problem of maximizing a quadratic form 〈Ax,x〉 subject to ‖x‖q=1, where A has matrix entries View the MathML source with i,j|k and q≥1. We investigate when the optimum is achieved at a ‘multiplicative’ point; i.e. where x1xmn=xmxn. This turns out to depend on both f and q, with a marked difference appearing as q varies between 1 and 2. We prove some partial results and conjecture that for f multiplicative such that 0

Socioeconomic correlates of global mammalian conservation status

The main causes of biodiversity decline are related to human use of resources, which is ultimately triggered by the socioeconomic decisions made by individuals and nations. Characterizing the socioeconomic attributes of areas in which biodiversity is most threatened can help us identify decisions and conditions that promote the presence or absence of threats and potentially suggest more sustainable strategies. In this study we explored how diverse indicators of social and economic development correlate with the conservation status of terrestrial mammals within countries explicitly exploring hypothesized linear and quadratic relationships. First, comparing countries with and without threatened mammals we found that those without threatened species are a disparate group formed by European countries and Small Island Developing States (SIDS) with little in common besides their slow population growth and a past of human impacts. Second, focusing on countries with threatened mammals we found that those with a more threatened mammalian biota have mainly rural populations, are predominantly exporters of goods and services, receive low to intermediate economic benefits from international tourism, and have medium to high human life expectancy. Overall, these results provide a comprehensive characterization of the socioeconomic profiles linked to mammalian conservation status of the world's nations, highlighting the importance of transborder impacts reflected by the international flux of goods, services and people. Further studies would be necessary to unravel the actual mechanisms and threats that link these socioeconomic profiles and indicators with mammalian conservation. Nevertheless, this study presents a broad and complete characterization that offers testable hypotheses regarding how socioeconomic development associates with biodiversity.

Improving power and accuracy of genome-wide association studies via a multi-locus mixed linear model methodology

Genome-wide association studies (GWAS) have been widely used in genetic dissection of complex traits. However, common methods are all based on a fixed-SNP-effect mixed linear model (MLM) and single marker analysis, such as efficient mixed model analysis (EMMA). These methods require Bonferroni correction for multiple tests, which often is too conservative when the number of markers is extremely large. To address this concern, we proposed a random-SNP-effect MLM (RMLM) and a multi-locus RMLM (MRMLM) for GWAS. The RMLM simply treats the SNP-effect as random, but it allows a modified Bonferroni correction to be used to calculate the threshold p value for significance tests. The MRMLM is a multi-locus model including markers selected from the RMLM method with a less stringent selection criterion. Due to the multi-locus nature, no multiple test correction is needed. Simulation studies show that the MRMLM is more powerful in QTN detection and more accurate in QTN effect estimation than the RMLM, which in turn is more powerful and accurate than the EMMA. To demonstrate the new methods, we analyzed six flowering time related traits in Arabidopsis thaliana and detected more genes than previous reported using the EMMA. Therefore, the MRMLM provides an alternative for multi-locus GWAS.

A new adaptive multiple modelling approach for non-linear and non-stationary systems

This paper proposes a novel adaptive multiple modelling algorithm for non-linear and non-stationary systems. This simple modelling paradigm comprises K candidate sub-models which are all linear. With data available in an online fashion, the performance of all candidate sub-models are monitored based on the most recent data window, and M best sub-models are selected from the K candidates. The weight coefficients of the selected sub-model are adapted via the recursive least square (RLS) algorithm, while the coefficients of the remaining sub-models are unchanged. These M model predictions are then optimally combined to produce the multi-model output. We propose to minimise the mean square error based on a recent data window, and apply the sum to one constraint to the combination parameters, leading to a closed-form solution, so that maximal computational efficiency can be achieved. In addition, at each time step, the model prediction is chosen from either the resultant multiple model or the best sub-model, whichever is the best. Simulation results are given in comparison with some typical alternatives, including the linear RLS algorithm and a number of online non-linear approaches, in terms of modelling performance and time consumption.

The multiple team formation problem using sociometry

The Team Formation problem (TFP) has become a well-known problem in the OR literature over the last few years. In this problem, the allocation of multiple individuals that match a required set of skills as a group must be chosen to maximise one or several social positive attributes. Speci�cally, the aim of the current research is two-fold. First, two new dimensions of the TFP are added by considering multiple projects and fractions of people's dedication. This new problem is named the Multiple Team Formation Problem (MTFP). Second, an optimization model consisting in a quadratic objective function, linear constraints and integer variables is proposed for the problem. The optimization model is solved by three algorithms: a Constraint Programming approach provided by a commercial solver, a Local Search heuristic and a Variable Neighbourhood Search metaheuristic. These three algorithms constitute the first attempt to solve the MTFP, being a variable neighbourhood local search metaheuristic the most effi�cient in almost all cases. Applications of this problem commonly appear in real-life situations, particularly with the current and ongoing development of social network analysis. Therefore, this work opens multiple paths for future research.